WASHINGTON (CNN) -- The Bush administration wants a federal court and congressional committees not to pursue investigations into the destruction of videotapes showing CIA interrogations of two al Qaeda suspects.

Attorney General Michael Mukasey speaks with President Bush at the White House on Wednesday.

It says the inquiries would interfere with an ongoing probe by the Justice Department in collaboration with the CIA.

Defense attorneys for some terror suspects have asked U.S. District Judge Henry Kennedy to look into whether the tapes' destruction violated a June order.

The measure requires the government to preserve evidence and information regarding detainees held at Guantanamo Bay, Cuba.

But Friday night, the Bush administration urged Kennedy not to hold that inquiry, saying the tapes were not covered by the order because one of the detainees videotaped -- Osama bin Laden lieutenant Abu Zubaydah -- was not at Guantanamo Bay in June.

Also Friday, CIA Inspector General John Helgerson and assistant Attorney General Kenneth Wainstein sent a letter to the top Democrat and Republican on the House Select Committee on Intelligence, urging the panel to abandon its investigation because of the inspector general and Justice Department probe.

"We cannot estimate how long this process will take or where it will lead, but pledge to advise you as soon as we conclude that our efforts are no longer at risk or that these requests can be fulfilled without jeopardizing our inquiry," says the letter to committee Chairman Silvestre Reyes and ranking Republican member Peter Hoekstra. Watch a report on the dispute and the requests to delay investigations »

House Intelligence Committee leaders have said the executive branch cannot be trusted to oversee itself.

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But CIA spokesman Mark Mansfield said Saturday, "the CIA will cooperate fully with both the preliminary inquiry by the Department of Justice and the CIA Inspector General as well as with the Congress. That has been, and certainly continues to be the case."

Lawmakers continued their criticism Saturday.

"The continuing saga of cover-up and delay by this administration must be stopped before more documents are lost to future investigators," said Sen. Joe Biden, D-Delaware, a presidential candidate.

Attorney General Michael Mukasey on Friday rejected demands from key congressional leaders for information about the Justice Department's preliminary inquiry, saying turning over the information might be seen as bowing to "political influence."

In letters to the House and Senate Judiciary committees, Mukasey said he would not turn over the material, nor would he appoint a special prosecutor to conduct the investigation, as some lawmakers had requested.

"At my confirmation hearing, I testified that I would act independently, resist political pressure and ensure that politics plays no role in cases brought by the Department of Justice," Mukasey said.

"Consistent with that testimony, the facts will be followed wherever they lead in this inquiry and the relevant law applied."

He sent a third similar letter to Assistant Senate Majority Leader Richard Durbin, D-Illinois, who had been the first to issue demands for information from the Justice Department.

"With regard to the suggestion that I appoint a special counsel, I am aware of no facts at present to suggest that department attorneys cannot conduct this inquiry in an impartial manner. If I become aware of information that leads me to a different conclusion, I will act on it," Mukasey said.

Senate Judiciary Committee Chairman Patrick Leahy, D-Vermont, said he was disappointed by the decision and indicated a confrontation with the new attorney general would come early next year.

He also suggested that access to the CIA tape inquiry will be an issue when Mukasey's nominated deputy, Mark Filip, comes before the panel for a confirmation hearing next week.

The tapes -- showing then-newly approved "alternative" interrogation techniques -- were recorded in 2002, CIA Director Michael Hayden said earlier this month in a letter to CIA employees.

The CIA made the decision to destroy the tapes in 2005 "only after it was determined they were no longer of intelligence value and not relevant to any internal, legislative, or judicial inquiries," Hayden said.

White House officials have said the president did not learn about the destruction of the tapes until last week.

The preliminary inquiry is to determine "whether further investigation is warranted," the Justice Department's assistant attorney general for national security, Kenneth L. Wainstein, said Saturday in a letter to the CIA's top lawyer, John Rizzo.E-mail to a friend